How can I rig an asymmetrical mesh?
Using automatic weights when assigning an armature to a mesh will assign weights to the existing mesh at that time, it will not automatically add weights to any modifications made after being applied.

By making changes to your mesh after rigging, you will need to manually weight paint the changes or redo the parenting with automatic weights to the new mesh. By reassigning the armature to the mesh you won't get duplicate armature modifiers or vertex groups, but you will most likely loose any manual adjustments you may have made to weight painting after doing automatic weights.